A polynomial time algorithm for diophantine equations in one variable

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Abstract

We exhibit an algorithm computing, for a polynomial f ∈ ℤ [t], the set of its integer roots. The running time of the algorithm is polynomial in the size of the sparse encoding of f.

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Cucker, F., Koiran, P., & Smale, S. (1999). A polynomial time algorithm for diophantine equations in one variable. Journal of Symbolic Computation, 27(1), 21–29. https://doi.org/10.1006/jsco.1998.0242

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